9514 1404 393
Answer:
a factor of 2 is shown, but 4 was factored out
Step-by-step explanation:
The difference of squares is factored as ...
a² -b² = (a +b)(a -b)
Then the given difference of squares factors as ...
144x² -100 = (12x)² -10² = (12x +10)(12x -10)
Each of these factors has a factor of 2 that can be factored out:
= (2(6x +5))(2(6x -5))
= (2·2)(6x +5)(6x -5)
= 4(6x +5)(6x -5)
The first factor should be 4, not 2.
The complete question in the attached figure
Part a)
we know that
ABC is a right triangle
∠ACB=45°
AC=hypotenuse------> 6√2 cm
sin 45=AB/AC-----> AB=AC*sin 45----> AB=6√2*√2/2----> AB=6 cm
the answer part a) isAB=6 cmPart b)
we know that
volume of the pyramid=(1/3)*Area of the base*height
area of the base=50 cm²
height=6 cm
so
volume of the pyramid=(1/3)*50*6----> 100 cm³
the answer part b) is 100 cm³
Answer:
an = 2·2^(n-1)
Step-by-step explanation:
There are simple tests to determine whether a sequence is arithmetic or geometric. The test for an arithmetic sequence is to check to see if the differences between terms are the same. Here the differences are 2, 4, 8, so are not the same.
The test for a geometric sequence is to check to see if the ratios of terms are the same. Here, the ratios are ...
4/2 = 2
8/4 = 2
16/8 = 2
These ratios are all the same (they are "common"), so the sequence is geometric.
The general term of a geometric sequence with first term a1 and common ratio r is ...
an = a1·r^(n-1)
Filling in the values for this sequence, we find the general term to be ...
an = 2·2^(n-1)